A222564 Least integer that is a sum of 2*k - 1 consecutive primes for k = 1..n.

2, 23, 83, 311, 28382041, 1128722657, 460787266801

Offset: 1

Author

Zak Seidov, Feb 27 2013

Keywords

• nonn
• more

Comments

For a(5) = 28382041, the first members of the sets are 9460669, 5676371, 4054499, and 3153499.

For a(6) the first members of the sets are 376240871, 225744509, 161246051, 125413559 and 102611081. For a(7) they are 153595755589, 92157453257, 65826752333, 51198585101, 41889751411 and 35445174181 - Giovanni Resta, Feb 27 2013

Examples

			a(1) = 2;
a(2) = 23 = 5 + 7 + 11;
a(3) = 83 = 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23;
a(4) = 311 = 101 + 103 + 107 = 53 + 59 + 61 + 67 + 71 = 31 + 37 + 41 + 43 + 47 + 53 + 59.
		

Crossrefs

Cf. A222592.

Programs

Mathematica

pr = Prime[Range[1000]]; tu[n_]:=(Total /@ Partition[pr, n, 1])
Intersection[tu[3],tu[5],tu[7]][[1]] (* gives a(3) = 311 - Zak Seidov, Feb 27 2013*)
a[n_] := If[n == 1, 2, Block[{t, w}, t = Table[{Total@(w = Prime@ Range@(2*i + 1)), w}, {i, n - 1}]; While[Length@Union[First /@ t] > 1 || ! PrimeQ@t[[1, 1]], t = Sort@t; w = NextPrime@t[[1, 2, -1]]; t[[1, 1]] += w - t[[1, 2, 1]]; t[[1, 2]] = Append[Rest@t[[1, 2]], w]]; t[[1, 1]]]]; Array[a, 4] (* Giovanni Resta, Feb 27 2013 *)

Extensions

a(6)-a(7) from Giovanni Resta, Feb 27 2013